It can't be "more than two years old," since it the 6th gen iPod nano was released a littile less than two years ago. But unless you bought AppleCare with it (and it's more than ONE year old), I guess it is still out of warranty...
That "diagnostic mode N20" is no "weird" mystery. It can be accessed using this procedure
Doing a Reset
should (normally) restart the iPod and take you out of this mode. You've probably done the Reset, but did you (or the Apple Store person) do a Restore of the iPod in iTunes. Select iPod in iTunes sidebar, under DEVICES. Over to the right, go to the Summary tab. There is a Restore button there. This will erase the iPod, re-install its software, and set it to default settings. If a software glitch is causing this problem, it should be fixed.